Create an edge parallel to the normal of a face from a given vertex
You could use the View orientation, and set an orthographic view to the face, side on, with ShiftNumpad 1 or ShiftNumpad 3.. but I still think the quickest way is with a Custom Orientation. You don't need to duplicate a face to create an orientation from it


Right-click on the '+' in the Orientation dropdown, and add it to your Quick Menu, and/or give it a keyboard shortcut. (It used to be CtrlAltSpacebar)
In the Adjust Last Operation panel, set the New Orientation op. to 'Use After Creation' and 'Overwrite Previous'
You would have to select a face in any case, to avoid ambiguity, so do that...
.. and use your shortcut, followed by vertex selection, and EZ


or

You could try using the Cursor.


In the Cursor tool, set its Orientation option to 'Geometry'
and check 'Surface Project'
Give yourself  reachable keyboard shortcuts for the Cursor tool, and the Tweak select tool
Using the shortcuts, and with the Transform Orientation set to 'Cursor', drag the cursor over the face of interest, and EZ the vertex.